Turbine engine with a blade

ABSTRACT

A blade for a turbine engine with a wall separating a cooling fluid flow and a hot gas fluid flow and having a heated surface along which the hot gas fluid flow flows and a cooled surface facing the cooling fluid flow. A plurality of cooling holes each having a passage extending between an inlet at the cooled surface and an outlet at the heated surface. The outlet extending between an upstream end and a downstream end with respect to the hot gas fluid flow to define a distance, the passage defining a centerline forming a first angle (θ) with the heated surface.

TECHNICAL FIELD

The present subject matter relates generally to a blade for a turbineengine, and more specifically to a blade with cooling hole and geometricfeatures.

BACKGROUND

A gas turbine engine typically includes a turbomachine, with a fan insome implementations. The turbomachine generally includes a compressor,combustor, and turbine in serial flow arrangement. The compressorcompresses air which is channeled to the combustor where it is mixedwith fuel. The mixture is then ignited for generating hot combustiongases. The combustion gases are channeled to the turbine, which extractsenergy from the combustion gases for powering the compressor and fan, ifused, as well as for producing useful work to propel an aircraft inflight or to power a load, such as an electrical generator.

During operation of the gas turbine engine, various systems can generatea relatively large amount of heat. For example, a substantial amount ofheat can be generated during operation of the thrust generating systems,lubrication systems, electric motors and/or generators, hydraulicsystems or other systems. Accordingly, cooling mechanisms for the enginecomponents therein is advantageous.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present disclosure, including thebest mode thereof, directed to one of ordinary skill in the art, is setforth in the specification, which makes reference to the appendedfigures, in which:

FIG. 1 is a schematic cross-sectional view of a gas turbine engine inaccordance with an exemplary embodiment of the present disclosure.

FIG. 2 is a schematic cross-sectional view of a turbine section of thegas turbine engine of FIG. 1 in accordance with an exemplary embodimentof the present disclosure.

FIG. 3 is a perspective view of a turbine blade suitable for the turbineengine from FIG. 1 in accordance with various aspects described herein.

FIG. 4 is a schematic cross-sectional view illustrating a representationof a portion of the tip for the turbine blade of FIG. 3 along lineIV-IV.

FIG. 5 is a cross-sectional view illustrating a set of cooling holesfrom the turbine blade of FIG. 3 along line V-V in accordance withvarious aspects described herein.

FIG. 6 is a schematic cross-sectional view of overlapping cooling holegeometries having varying surface angles, layback angles, and diffuserangles in accordance with various aspects described herein.

FIG. 7 is a graph illustrating a first exemplary range of values forsurface angles, layback angles, and diffuser angles in accordance withvarious aspects described herein.

FIG. 8 is a graph illustrating a second exemplary range of values forsurface angles, layback angles, and diffuser angles in accordance withvarious aspects described herein.

DETAILED DESCRIPTION

Reference will now be made in detail to present embodiments of thedisclosure, one or more examples of which are illustrated in theaccompanying drawings. The detailed description uses numerical andletter designations to refer to features in the drawings. Like orsimilar designations in the drawings and description have been used torefer to like or similar parts of the disclosure.

Aspects of the disclosure generally relate to turbine engine airfoils,including cooled turbine engine blades. Traditional blades often includefilm cooling over portions of the blade surface, where tip coolingarrangements are generally separated from radially-inward coolingarrangements due to design constraints. Aspects of the disclosureprovide for a blade with an integrated cooling design for both tipregions and lower-span regions, providing for improved coolingperformance at higher-temperature operations. Aspects of the disclosurealso provide for a blade with a generally smooth or flat exteriorsurface, providing improved aerodynamic performance while allowing fordesired cooling effectiveness in high-temperature environments.

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any implementation described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other implementations. Additionally, unlessspecifically identified otherwise, all embodiments described hereinshould be considered exemplary.

As may be used herein, the terms “first,” “second,” and “third” can beused interchangeably to distinguish one component from another and arenot intended to signify location or importance of the individualcomponents.

The terms “forward” and “aft” as may be used herein, refer to relativepositions within a gas turbine engine or vehicle, and refer to thenormal operational attitude of the gas turbine engine or vehicle. Forexample, with regard to a gas turbine engine, forward refers to aposition closer to an engine inlet and aft refers to a position closerto an engine nozzle or exhaust.

The terms “upstream” and “downstream” refer to the relative directionwith respect to a flow in a pathway. For example, with respect to afluid flow, “upstream” refers to the direction from which the fluidflows, and “downstream” refers to the direction to which the fluidflows.

The term “fluid” can be a gas or a liquid. The term “fluidcommunication” means that a fluid is capable of making the connectionbetween the areas specified.

The singular forms “a”, “an”, and “the” include plural references unlessthe context clearly dictates otherwise.

As may be used herein, an “additively manufactured” component will referto a component formed by an additive manufacturing (AM) process, whereinthe component is built layer-by-layer by successive deposition ofmaterial. AM is an appropriate name to describe the technologies thatbuild 3D objects by adding layer-upon-layer of material, whether thematerial is plastic, ceramic, or metal. AM technologies can utilize acomputer, 3D modeling software (Computer Aided Design or CAD), machineequipment, and layering material. Once a CAD sketch is produced, the AMequipment can read in data from the CAD file and lay down or addsuccessive layers of liquid, powder, sheet material or other material,in a layer-upon-layer fashion to fabricate a 3D object. It should beunderstood that the term “additive manufacturing” encompasses manytechnologies including subsets like 3D Printing, Rapid Prototyping (RP),Direct Digital Manufacturing (DDM), layered manufacturing and additivefabrication. Non-limiting examples of additive manufacturing that can beutilized to form an additively-manufactured component include powder bedfusion, vat photopolymerization, binder jetting, material extrusion,directed energy deposition, material jetting, or sheet lamination. It isalso contemplated that a process utilized could include printing anegative of the part, either by a refractory metal, ceramic, or printinga plastic, and then using that negative to cast the component.

All directional references (e.g., radial, axial, proximal, distal,upper, lower, upward, downward, left, right, lateral, front, back, top,bottom, above, below, vertical, horizontal, clockwise, counterclockwise,upstream, downstream, forward, aft, etc.) are only used foridentification purposes to aid the reader's understanding of the presentdisclosure, and do not create limitations, particularly as to theposition, orientation, or use of aspects of the disclosure describedherein. Connection references (e.g., attached, coupled, connected, andjoined) are to be construed broadly and can include intermediatestructural elements between a collection of elements and relativemovement between elements unless otherwise indicated. As such,connection references do not necessarily infer that two elements aredirectly connected and in fixed relation to one another. The exemplarydrawings are for purposes of illustration only and the dimensions,positions, order and relative sizes reflected in the drawings attachedhereto can vary.

As used herein, “flow field” refers to a distribution of at least one ofa fluid density or fluid velocity in a given spatial region.

As used herein, a stage of either the compressor or turbine is a pair ofan adjacent set of blades and set of vanes in a flow direction, withboth sets of the blades and vanes circumferentially arranged about anengine centerline. The blades rotate relative to the engine centerlineand, in one example, are mounted to a rotating structure, such as adisk, to affect the rotation. A pair of circumferentially-adjacent vanesin the set of vanes are referred to as a nozzle. The vanes, in oneexample, are stationary, and mounted to a casing surrounding the set ofblades, and, in another example of a counter-rotating engine, aremounted to a rotating drum surrounding the set of blades. The rotationof the blades creates a flow of air through the vanes/nozzles.

As used herein, a “number of blades” (denoted “NB”) is the number ofblades in a stage within either the combustor or turbine of a turbineengine of an aircraft.

As used herein, a “number of nozzles” (denoted “NN”) is the number ofnozzles in a stage. Put another way, the number of nozzles NN in a stagewill be half the number of vanes in that stage.

As may be used herein, “indicated turbine exhaust gas temperature” or“exhaust gas temperature” (denoted “EGT”) refers to a maximum gastemperature in a turbine engine as measured at a location between ahigh-pressure turbine and a low-pressure turbine under takeoff powerconditions during a 5-minute period.

As used herein, “tip radius” (denoted “TR”) is the distance measuredfrom the engine centerline to a tip of the blades when the turbineengine is off under standard day conditions, e.g. 15° C. at mean sealevel altitude and 101.3 kPa atmospheric pressure, as is known in theart. Tip radius TR as used herein is also known in the art as a “coldtip radius.”

As may be used herein, a “percent span,” or “percent of span,” e.g. 50%span, 80% span, 100% of span, or the like, refers to a location along ablade expressed in terms of a percentage of an overall span-wise lengthof a blade, as measured from a tip to a root. For example, “10% span”refers to a location along the blade that is spaced from the tip by 10%of the overall span-wise length of that blade. Put another way, “10%span” refers to a location along the blade that is spaced from the rootby 90% of the overall span-wise length.

As used herein, “radial” or “radially” refers to a span-wise directiondefined between a blade root and a blade tip. In some implementations,the span-wise direction is non-orthogonal to an engine centerline. Insome implementations, the span-wise direction is orthogonal to an enginecenterline.

As used herein, “blade parameter” (denoted “BP”) is a value describingthe smoothness of the blade along a pressure side of the blade. Theblade parameter BP is a ratio between a blade surface length, or surfacelength (denoted “L_(max)”) and a radial length (denoted “R”) between twopoints lying on the blade surface. The radial length R is astraight-line/radial distance measured radially along the pressure-sidesurface between two locations that share a common chord-wise position.The surface length L_(max) measures the length of a pressure-sidesurface between the same two locations as R. Put another way, Rrepresents a distance between two points on a flat blade surface, andL_(max) is a contour or length portion of the blade surface between thesame two points taken over the blade surface, the length measured toinclude indents or protrusions on the blade surface, and excluding anycooling holes, slots, or other apertures that extend through the bladesurface. When the ratio L_(max)/R is equal to 1, the blade is smooth orhas a flat surface. When the ratio L_(max)/R is greater than 1, anindent or a protrusion exists on the blade, such as a shelf on the bladesurface. The blade parameter BP describes the flatness of the bladebetween the two points.

As used herein, Blade Tip Durability Factor (denoted “BTDF”) is a valuedescribing a relationship between the number of blades NB, number ofnozzles NN, exhaust gas temperature EGT, tip radius TR, and bladeparameter BP.

As used herein a “hydraulic diameter” is in reference to the openingswithin the unit-cell. Hydraulic diameter is a commonly used term whenhandling flow in non-circular tubes and channels. When the cross-sectionis uniform along the tube or channel length, it is defined as

$D_{H} = \frac{4a}{p}$

where “a” is the cross-sectional area of the flow and “p” is the wettedperimeter of the cross-section.

A straight-line length referred to herein as distance (denoted “d” withvarious subscripts) is a length measured along a straight-line between adownstream end and an upstream end of the referenced cooling holeoutlets.

A first angle, referred to herein as a surface angle (θ) is formedbetween a centerline CL of the referenced cooling holes and a heatedsurface as denoted in FIG. 5 .

A second angle, referred to herein as a layback angle (β) is formedbetween a line extending from a bottom wall of the referenced coolingholes and a layback surface as denoted in FIG. 5 .

A third angle, referred to herein as a diffuser angle (Δ) is formedbetween the straight-line length and the layback surface at thedownstream end of the referenced cooling holes as denoted in FIG. 5 .

In certain exemplary embodiments of the present disclosure, a gasturbine engine defining a centerline and a circumferential direction isprovided. The gas turbine engine can generally include a rotor assemblyand a stator assembly. The rotor assembly and the stator assembly cancollectively define a substantially annular flowpath relative to thecenterline of the gas turbine engine. The rotor assembly can include aset of blades. The set of blades extend from a disk and can bedistributed circumferentially about the engine centerline. It is furthercontemplated that the set of blades can be any number of blades mountedto the disk. The stator assembly includes a set of vanes. The set ofvanes extend between inner and outer bands and are distributedcircumferentially about the centerline. The set of vanes also defines aset of nozzles. It is further contemplated that the set of vanesincludes a single pair of vanes defining a single nozzle. Rotation ofthe disk causes the set of blades to produce a fluid flow through theset of nozzles.

The number of blades NB and the number of nozzles NN for a stage areboth contributors to controlling a flow field across each blade andthrough the nozzles. The tip radius TR sets a tip clearance value alongwith a tip rotational speed. For instance, material properties of theblade such as shear, thermal expansion, or the like can affect the tipclearance value at high rotational speeds. In this manner, the number ofblades NB, number of nozzles NN, and tip radius TR are integral to theneed for certain specific cooling on the blade during operation.

In addition, it can be appreciated that multiple engine operatingfactors have an effect on blade cooling and aerodynamic performance at agiven location within the engine. For instance, upstream nozzleconfigurations establish the incoming airflow to the blades at a givenstage. Nozzles can produce varying-temperature wakes, such as a nozzleexit “hot-cold-hot” wake, that a downstream blade then rotates throughduring operation. Such nozzle-exit wakes or flow features defineincoming flow boundary conditions onto the downstream blade, and alsodetermine a primary condition for setting the blade thermal environmentthat leads to a blade cooling performance condition.

Another factor to be considered is that the number of blades NB on thedisk sets a limit on an overall chord-wise width of each blade,including a chord-wise width of the blade tip. For example, a low numberof blades per disk provides for longer chord-wise tip widths, and a highnumber of blades per disk leads to shorter chord-wise tip widths. It canbe appreciated that wider blade tips can require more cooling holes,cooling rows, or larger spacing between a fixed number of cooling holes,to achieve a given cooling performance over the wider surface.

Still another factor to be considered is that the tip radius TR of theblade impacts the clearance between the rotating blade and thestationary outer wall adjacent the tip. A larger clearance will allowfor more hot flow to go over the tip of the blade during operation, anda smaller clearance will allow less hot flow to go over the tip. It canbe appreciated that a larger tip clearance, with more hot flow over thetip, warrants a higher amount of cooling needed for the blade. The bladetip clearance value is used to determine a specific selection of tiphole placement, spacing, patterning, or the like.

The standard practice for solving the nozzle-exit wake problem has beento design cooling hole outlet patterns for the turbine engine using abaseline condition, e.g. “flight idle,” then select a cooling holelayout for the blade at its particular location within the engine, andthen verify whether the blade will operate in an acceptable manneracross a flight envelope, including from a cooling-performanceperspective and an aerodynamic-performance perspective. Such coolinghole layouts are often designed with respect to a baseline bladegeometric profile, which can include a baseline pressure-sidesmoothness.

The inventors' practice has proceeded in the manner of designing aturbine engine with a given number of blades and nozzles, modifying acooling hole layout on the blade in a particular engine stage, testingthe engine with the cooling hole layout for meeting coolingrequirements, redesigning the turbine engine (number of stages, blades,nozzles, or the like), if needed, to meet cooling requirements, thenchecking the cooling performance again. This process can continue forlong periods of time until a workable blade design is identified. Theabove-described iterative process is then repeated for the design ofseveral different types of turbine engines in which the blade will beutilized, such as those shown in the following FIGS. 1 and 2 . In otherwords, an engine can meet the cooling performance requirements but notanother necessary benchmark. Examples of the turbine engine and coolinghole layouts developed by the inventors follows.

Referring now to the drawings, FIG. 1 is a schematic view of a turbineengine 10. As a non-limiting example, the turbine engine 10 can be usedwithin an aircraft. The turbine engine 10 can include, at least, acompressor section 12, a combustor 14, and a turbine section 16. A fan11 is also provided in the engine 10 for providing inlet air to thecompressor section 12. A drive shaft 18 rotationally couples the fan 11,compressor section 12, and turbine section 16, such that rotation of oneaffects the rotation of the others, and defines a rotational axis orcenterline 20 for the turbine engine 10.

The compressor section 12 includes a low-pressure (LP) compressor 22 anda high-pressure (HP) compressor 24 serially fluidly coupled to oneanother. The turbine section 16 includes an HP turbine 26 and a LPturbine 28 serially fluidly coupled to one another. The drive shaft 18operatively couples the LP compressor 22, the HP compressor 24, the HPturbine 26 and the LP turbine 28 together. In some implementations, thedrive shaft 18 includes an LP drive shaft (not illustrated) and an HPdrive shaft (not illustrated), where the LP drive shaft couples the LPcompressor 22 to the LP turbine 28, and the HP drive shaft couples theHP compressor 24 to the HP turbine 26. An LP spool be defined as thecombination of the LP compressor 22, the LP turbine 28, and the LP driveshaft such that the rotation of the LP turbine 28 applies a drivingforce to the LP drive shaft, which in turn rotates the LP compressor 22.An HP spool can be defined as the combination of the HP compressor 24,the HP turbine 26, and the HP drive shaft such that the rotation of theHP turbine 26 applies a driving force to the HP drive shaft which inturn rotates the HP compressor 24.

While not illustrated, it will be appreciated that the turbine engine 10can include other components, such as, but not limited to a gearbox. Asa non-limiting example, the gearbox can be located at any suitableposition within the turbine engine such that it connects one rotatingportion to another. As a non-limiting example, the gearbox can connectthe fan 11 to the drive shaft 18. The gearbox can allow the fan 11 torun at a different speed than the remainder of the turbine engine 10.

The compressor section 12 includes a plurality of axially spaced stages.Each stage includes a set of circumferentially-spaced rotating bladesand a set of circumferentially-spaced stationary vanes. In oneconfiguration, the compressor blades for a stage of the compressorsection 12 is mounted to a disk, which is mounted to the drive shaft 18.Each set of blades for a given stage can have its own disk. In oneimplementation, the vanes of the compressor section 12 is mounted to acasing which extends circumferentially about the turbine engine 10. In acounter-rotating turbine engine, the vanes are mounted to a drum, whichis similar to the casing, except the drum rotates in a directionopposite the blades, whereas the casing is stationary. It will beappreciated that the representation of the compressor section 12 ismerely schematic and that there can be any number of stages. Further, itis contemplated that there can be any other number of components withinthe compressor section 12.

Similar to the compressor section 12, the turbine section 16 includes aplurality of axially spaced stages, with each stage having a set ofcircumferentially-spaced, rotating blades and a set ofcircumferentially-spaced, stationary vanes. In one configuration, theturbine blades for a stage of the turbine section 16 are mounted to adisk which is mounted to the drive shaft 18. Each set of blades for agiven stage can have its own disk. In one implementation, the vanes ofthe turbine section are mounted to the casing in a circumferentialmanner. In a counter-rotating turbine engine, the vanes can be mountedto a drum, which is similar to the casing, except the drum rotates in adirection opposite the blades, whereas the casing is stationary. It isnoted that there can be any number of blades, vanes and turbine stagesas the illustrated turbine section is merely a schematic representation.Further, it is contemplated that there can be any other number ofcomponents within the turbine section 16.

The combustor 14 is provided serially between the compressor section 12and the turbine section 16. The combustor 14 is fluidly coupled to atleast a portion of the compressor section 12 and the turbine section 16such that the combustor 14 at least partially fluidly couples thecompressor section 12 to the turbine section 16. As a non-limitingexample, the combustor 14 is fluidly coupled to the HP compressor 24 atan upstream end of the combustor 14 and to the HP turbine 26 at adownstream end of the combustor 14.

During operation of the turbine engine 10, ambient or atmospheric air isdrawn into the compressor section 12 via the fan 11 upstream of thecompressor section 12, where the air is compressed defining apressurized air. The pressurized air then flows into the combustor 14where the pressurized air is mixed with fuel and ignited, therebygenerating combustion gases. Some work is extracted from thesecombustion gases by the HP turbine 26, which drives the HP compressor24. The combustion gases are discharged into the LP turbine 28, whichextracts additional work to drive the LP compressor 22, and the exhaustgas is ultimately discharged from the turbine engine 10 via an exhaustsection (not illustrated) downstream of the turbine section 16. Thedriving of the LP turbine 28 drives the LP spool to rotate the fan 11and the LP compressor 22. The pressurized airflow and the combustiongases together define a working airflow that flows through the fan 11,compressor section 12, combustor 14, and turbine section 16 of theturbine engine 10.

Turning to FIG. 2 , a portion of the turbine section 16 is schematicallyillustrated. The turbine section 16 includes blades 30 mounted tocorresponding disks 32. Any number of individual blades 30 can bemounted to each disk 32. In some implementations, the blades 30 extendfrom the disk 32 orthogonally to the engine centerline 20. In someimplementations, the blades 30 extend from the disk 23 non-orthogonallyto the engine centerline 20.

Stationary vanes 34 are mounted to a stator ring 36 located axiallydownstream from each of the disks 32. A nozzle 38 is defined bycircumferentially-adjacent pairs of vanes 34. Any number of nozzles 38can be provided on the stator ring 36. In one exemplary configuration,each disk 32 includes at least 60 blades 30, including between 60-70blades 30, or up to 64 blades 30, in non-limiting examples. Each statorring 36 includes at least 38 nozzles 38, including between 38-50 nozzles38, or up to 42 nozzles 38, in non-limiting examples.

During operation of the engine 10, a flow of hot gas (denoted “H”) exitsthe combustor 14 and enters the turbine section 16. Various temperaturesensors can be provided for measuring a flow of hot gas temperature atlocations within the engine 10. In one example, an EGT sensor 40 islocated between the LP turbine 28 and the HP turbine 26. The EGT sensor40 senses, detects, or measures a temperature of the flow of hot gas Hat the indicated location. Multiple EGT sensors 40 can be provided.

For engine performance, the design of the geometry of an individualblade 30 is a function of the temperature of the flow of hot gas H at ornear the location of the blade 30, such as within two stages of theblade 30. By way of non-limiting example, an exemplary blade 30 in FIG.2 has a geometric profile based on the temperature of the flow of hotgas H as measured by the EGT sensor 40.

FIG. 3 is a perspective view of an exemplary blade assembly 42 that canbe utilized in the turbine engine 10 (FIG. 1 ). The blade assembly 42can include a dovetail 44 and the blade 30. A platform 46 lies betweenthe dovetail 44 and the blade 30 and can provide a mounting surface forthe blade 30. When multiple blades 30 are circumferentially arranged inside-by-side relationship, the platform 46 can radially contain the flowof hot gas H and forms the radially inner wall of an annulus throughwhich the flow of hot gas H flows. The dovetail 44 can be configured tomount to the disk 32 (FIG. 2 ) or similar structure of the engine 10.The dovetail 44 can further include at least one inlet passage 48extending through the dovetail 44 to provide internal fluidcommunication with the blade 30.

The blade 30 includes an outer wall 50 bounding an interior 52 andhaving an exterior surface 54. The blade 30 includes a concave-shapedpressure side 56 and a convex-shaped suction side 58 (hidden from view)which are joined together to define an airfoil cross-sectional shape ofthe blade 30 extending between a leading edge 60 and a trailing edge 62to define a chord-wise direction (denoted “CW”).

The outer wall 50 forms a root 64 where the blade 30 meets the platform46. The blade 30 extends radially outward from the root 64 to a tip 66to define a span-wise direction (denoted “S”). In some examples thespan-wise direction S is non-orthogonal to the engine centerline 20(FIG. 2 ), such as for blades 30 having a radial curvature between theroot 64 and tip 66.

A span-wise length (denoted “L”) is indicated for the blade 30 betweenthe tip 66 and the root 64 as shown. In addition, a tip radius TR isindicated between the tip 66 and a center of rotation for the blade 30,as indicated with truncated dashed line from the engine centerline 20.

The interior 52 of the blade 30 can include at least one cooling supplyconduit 76, illustrated in dashed line. The cooling supply conduit 76can be fluidly coupled with the inlet passage 48. At least one coolinghole 78 can be located along any portion of the outer wall 50 includingproximate the leading edge 60 and/or the trailing edge 62 asillustrated. The at least one cooling hole 78 can be part of a set ofcooling holes 80 passing through a substrate, which by way ofillustration is outer wall 50. The set of cooling holes 80 can define aplurality of cooling holes where there are three or more cooling holes78 local to each other. It should be understood, however, that thesubstrate can be any wall within the engine 10 including but not limitedto interior walls, a tip wall, or a combustion liner wall. The at leastone cooling hole terminates along a heated surface 82 defined by theouter wall 50. The heated surface 82 faces the flow of hot gas H duringoperation. The at least one inlet passage 48 is fluidly coupled to theset of cooling holes 80 to provide a cooling fluid flow (denoted “CF”)for cooling the heated surface 82.

Materials used to form the substrate and the structural segment caninclude, but are not limited to, steel, refractory metals such astitanium, or superalloys based on nickel, cobalt, or iron, and ceramicmatrix composites, or combinations thereof. The substrate and structuralsegment can be formed by a variety of methods, including additivemanufacturing, casting, electroforming, or direct metal laser melting,in non-limiting examples.

Some exemplary first and second locations (denoted “L1” and “L2”,respectively) are indicated on the outer wall 50. In the example shown,the first location L1 is at 10%, i.e. 10% of the span-wise length L, andthe second location L2 is at 0% of the span-wise length L. Put anotherway, the second location L2 is at the tip 66.

In addition, an exemplary chord line (denoted “C”) is indicated alongthe blade 30 between the leading edge 60 and trailing edge 62. Achord-wise position P (denoted “P”) is also indicated for the firstlocation L1 and the second location L2. The first and second locationsL1, L2 share a common chord-wise position between the leading edge 60and trailing edge 62. FIG. 3 shows the chord line C and span-wise lengthL as projected onto the plane of the paper. The chord-wise position P,the dashed line extending upwards from P, and the first and secondlocations L1, L2 reside in this plane.

Turning to FIG. 4 , a schematic cross-sectional view of the blade 30proximate the tip 66 along line IV-IV of FIG. 3 is shown. The pressureside 56 is illustrated along with a portion of the interior 52. Inaddition, an exemplary surface feature 70 is provided in the outer wall50. The surface feature 70 is shown in the form of an indent or recessin the outer wall 50. It is also contemplated that the surface feature70 can include, or alternatively take the form of a protrusion, such asa shelf, extending outwardly (right to left) from the outer wall 50. Thesurface feature 70 represents a deviation from a locally-flat outer wall50. Such a deviation also includes surface textures, such as bumps,divots, surface roughness, or the like that may be present on the outerwall 50.

A surface length (denoted “L_(max)”) is defined by a span-wise contourline along the outer wall 50 between the first location L1 and thesecond location L2, taken at the common chord-wise position P (FIG. 3 )as described above. The surface length L_(max) measures the span-wiselength of the pressure side surface contour, taken along the outer wall50 between L1 and L2, excluding any cooling holes, slots, or otherapertures that extend through the outer wall 50 into the interior 52.

A radial length (denoted “R”) is defined by a span-wise line extendingbetween the first location L1 and the second location L2. The surfacelength L_(max) and the radial length R along the span-wise direction Sare non-orthogonal to the engine centerline 20 (FIG. 3 ) in someimplementations. As can be understood from FIG. 4 , L_(max) is greaterthan R due to the presence of an indentation. Similarly, L_(max) will begreater than R when there is a protrusion, instead of an indentation. Asurface length and a radial length R are measured along the dashed line,which extends perpendicular to the line indicating the chord line C inFIG. 3 .

The surface length L_(max) and the radial length R are both defined atthe common chord-wise position P. The first and second locations L1, L2are illustrated in dashed line intersecting the outer wall 50, and theradial length R is indicated as being spaced from the surface lengthL_(max). It will be understood that this is for visual clarity purposesonly, and that both the surface length L_(max) and the radial length Rare defined at the common chord-wise position P. It can also beappreciated that the surface length L_(max) is greater than the radiallength R when the surface feature 70 is present in the outer wall 50.

Turning to FIG. 5 , a cross-section taken along line V-V from FIG. 3illustrates the set of cooling holes 80 within the outer wall 50. Theouter wall 50 defines the heated surface 82 facing the flow of hot gas Hand a cooled surface 84 facing the cooling fluid flow CF. The at leastone cooling hole 78, illustrated as two cooling holes can each include aconnecting passage 86 extending between an inlet 88 on the cooledsurface 84 and an outlet 90 on the heated surface 82. The outlet 90extends between a downstream end 92 and an upstream end 94. It should beunderstood that the outer wall 50 can be any substrate within the engine10 including but not limited to the platform 46 (FIG. 3 ), a tip wall,or a combustion liner wall. It is noted that although the outer wall 50is shown as being generally planar at the heated surface 82, and curvedalong the cooled surface 84, it should be understood that that the outerwall 50 can be curved or planar along any surface. The geometry of theat least one cooling hole 78 described herein can include thermalbarrier coating, bond-coat, or environmental coating for oxidation orcorrosion. It should be understood that the geometry discussed herein isfor a set of cooling holes 80 during operation whether that set includescoating or not.

The inlet 88 can define a centerline (denoted “CL”) extending from ageometric center 96 of the inlet 88 toward the outlet 90. The centerlineCL extends straight through the connecting passage 86 substantiallyparallel to a top wall 104 and out of the outlet 90, though notnecessarily through a geometric center of the outlet 90. As isillustrated by an extension of the centerline CL, a first angle,referred to herein as surface angles (θ₁, θ₂) is formed between thecenterline CL and the heated surface 82. The connecting passage 86 caninclude a metering section 98 having a circular cross section, though itcould have any cross-sectional shape. The metering section 98 can beprovided at or near the inlet 88, and extend along the connectingpassage 86 while maintaining a constant or nearly constantcross-sectional area (denoted “CA”). The metering section 98 defines thesmallest, or minimum cross-sectional area CA of the connecting passage86. The metering section 98 can be located anywhere within theconnecting passage 86 where the cross-sectional area CA is the smallestwithin the connecting passage 86. It is contemplated that the meteringsection 98 defines the inlet 88 and extends therefrom as illustrated toa metering end 99. The metering section 98 can define a metering length(denoted “Lm”) within the connecting passage 86. The metering length Lmis greater than zero. The metering section 98 is for metering of themass flow rate of the cooling fluid flow CF.

A diffusing section 100 can extend from the metering section 94 to theoutlet 90 within the connecting passage 86. The diffusing section 100can include a hood 102 having a diffused length (denoted “La”) measuredalong the centerline CL from the metering section 98 to the upstream end94 of the outlet 90. The connecting passage 86 can have a top wall 104and a bottom wall 106. The hood 102 defined by at least a portion of thetop wall 104. The diffusing section 100 can have a layback surface 110extending from the bottom wall 106 at a junction 105 to the heatedsurface 82 to define the downstream end 92 of the outlet 90. The laybacksurface 110 can define at least a portion of the outlet 90 and thediffusing section 100. The layback surface 110 can bend away from thebottom wall 106 at a second angle, referred to herein as layback angles(β₁,β₂). While illustrated as flat, it should be understood that thelayback surface 110 is not necessarily flat and that the anglesdescribed herein are with respect to an average slope of the laybacksurface 110 and the surface with which any of the angles herein aredescribed. The diffusing section 100 can enable diffusion into and outof the page between the metering end 99 and the junction 105. Diffusioncan continue into and out of the page as well as up and down withrespect to the page between the junction 105 and the outlet 90. It isfurther contemplated that the diffusion section 100 starts at thejunction 105.

The at least one cooling hole 78 provides fluid communication betweenthe cooling supply conduit 76 and the exterior surface 54. Duringoperation, the cooling fluid flow CF can be supplied via the inletpassages 48 (FIG. 3 ) and exhausted from the set of cooling holes 80 asa thin layer or film of cool air along the heated surface 82. While twocooling holes are shown in FIG. 5 , it is understood that thecross-sectional view can represent any one of or all of the coolingholes in the set of cooling holes 80.

The at least one cooling hole 78 can be a first cooling hole 78 a and asecond cooling hole 78 b. The first cooling hole 78 a can define a firstsurface angle (θ₁) and a first layback angle (β₁). The outlet 90 of thefirst cooling hole 78 a can extend a first distance (d₁) between thedownstream end 92 and the upstream end 94. The second cooling hole 78 bcan define a second surface angle (θ₂) and a second layback angle (β₂).The outlet 90 of the second cooling hole 78 b can extend a seconddistance (d₂) between the downstream end 92 and the upstream end 94. Thefirst and second distances (d₁, d₂) can be measured along astraight-line between the downstream and upstream ends 92, 94. Coolingholes with nearly constant layback angles (β) for any surface angle (β),in other words, where (β₁≈β₂) can have smaller outlets as the surfaceangle increases. To maximize cooling effectiveness, it was found to bebeneficial for the first and second distances (d₁, d₂), to beconsistent, that is nearly the same or equal along the outer wall 50 forall cooling holes 78.

In order to provide consistent cooling along the heated surface 82, thefirst and second distances (d₁, d₂) should be close to if not equal toeach other. In other words, (d₁≈d₂). It has been found that when thefirst distance (d₁) is within 5% of the second distance d₂, or when thefirst distance (d₁) is equal to the second distance (d₂), the mosteffective cooling along the heated surface 82 occurs. The set of coolingholes 80 can include three or more cooling holes 78 where (d₁≈d₃). Thisconsistency lends itself to uniform film cooling, which in turn improvescoating compensation. In order to maintain this consistency, severaliterations of cooling holes 78 with a given distance, by way ofnon-limiting example 2 mm, were made for various locations along theblade 30 with various curvatures. TABLE 1 includes three differentcooling holes all having the same distance. While these cooling holescan be arranged in a row, or sequential with respect to each other, itshould be understood that the distance value and the location on theblade 30 determines the surface angle (θ), layback angle (β) and thediffuser angle (Δ).

TABLE 1 Curvature d (mm) θ β Δ High 2 50° 37° 13° Low 2 22°  6° 16°Normal 2 30° 12° 18°

To achieve this consistency with the distance (d) and increase coolingeffectiveness, it was found unexpectedly and through a time-consumingiterative process, that while the surface angle (θ) changes with acurvature of the blade 30, the layback angle (β) and the diffuser angle(Δ) form an interdependent relationship. Geometrically, the differencebetween the surface angle (θ) and the layback angle (β) is the diffuserangle (Δ), in other words (Δ=θ−β). This relationship remains regardlessof whether the layback surface 110 is straight, or flat as illustrated.Therefore, as the surface angle increases either the layback angle (β)remains substantially constant or the diffuser angle (Δ).

Finding the balance between effective cooling with the set of coolingholes and the blade geometry described herein is a labor- andtime-intensive process, because the process is iterative and involvesthe selection of various cooling hole layouts designed for (in oneexample) flight idle, and then evaluating whether at other times inflight (e.g. non-flight idle) the cooling hole layout providesacceptable cooling for the blade. In some examples, the blade may have adifferent pressure-side smoothness compared to a baseline pressure-sidesmoothness on which the cooling hole layout was designed. Put anotherway, the cooling hole layout was often selected accordingly for variousblade configurations before a cooling hole layout was found thatsatisfies all design requirements: cooling performance, aerodynamicperformance, pressure ratio, rigidity, durability, thermal stresses,noise transmission levels, or the like.

For improved results, it is desirable to have consistent distancemeasurements as this promotes uniform surface cooling. In order toprovide consistent distance measurements (d₁, d₂) on various locationson the blade 30 described herein when the first and second surfaceangles (θ₁,θ₂) are not necessarily the same, a given range of anglevalues (α) for the first and second layback angles (β₁, β₂) as well asthe first and second diffuser angles (Δ₁, Δ₂) should be the same aboveand below a switch value (θ_(s)) of the surface angle (θ). The switchvalue (θ_(s)) is the value for the surface angle (θ) at which the rangesfor the layback angle (β) switch to the ranges of the diffuser angle (Δ)and vice versa. This was an unexpected result discovered during thecourse of engine designs that involved a time-consuming iterativeprocess, as previously described.

In one non-limiting example, the given range of angle values is(8°<α<20°). The first surface angle is 40 degrees (θ₁=40°) and thesecond surface angle is 25 degrees (θ₂=25°). The first layback angle is30 degrees (β₁=30°), giving a value of 10 degrees for the first diffuserangle (Δ₁=10°) and for the subsequent second cooling hole 78 b, thesecond layback angle is 10 degrees (β₂=10°), and the second diffuserangle is equal to 15 degrees (Δ₂=15°). The given range of angle values(8°<α<20°) is true for the value of the second layback angle(8°<β₂=10°<20°). The given range of angle values (8°<α<20°) is true forthe value of the first diffuser angle (8°<Δ₁=10°<20°). In this case, thegiven range of angle values (α) for the first and second layback angles(β₁, β₂) as well as the first and second diffuser angles (Δ₁, Δ₂) is thesame above and below the switch value (θ_(s)=28°). In other words, itwas found unexpectedly that maintaining the consistency for thedistances (d₁, d₂), for any range of angle values (α):(α_(low)<α<α_(hi)) where α_(hi)+α_(low)=θ_(s) can be summed up in twoif/then statements. The value of the surface angle (θ), the laybackangle (β) and the diffuser angle (Δ) are all related by the following:

If α_(hi)+α_(low)≤θ, then α_(low)<Δ<α_(hi)  (1)

If α_(hi)+α_(low)≥θ, then α_(low)<β<α_(hi)  (2)

Exemplary value ranges are shown in TABLE 2. As the range of angles (α)narrows (from the top row to the bottom row) the value at which thesurface angle (θ), flips from (1) to (2) decreases. Regions of the blade30 with high curvature, such as along the suction side 58 have largerranges, such as those in the first two rows of TABLE 2. Regions of theblade 30 with low curvature, such as along the pressure side 62 havesmaller ranges, such as those in the last two rows of TABLE 2.

TABLE 2 α_(low) α_(hi) α_(hi) + α_(low) θ Δ_(low) Δ_(hi) β_(low) β_(hi) 5º 40° 45° 50°  5º 40° 10° 45° 40°  0° 35°  5º 40° 10° 30° 40° 45º 10°30° 15° 35° 35°  5º 25° 10° 30° 10° 20° 30° 35° 10° 20° 15° 25° 25°  5º15º 10° 20° 12° 16° 28° 30° 12° 16° 14º 18° 20°  4º  8º 12° 16°

Turning to FIG. 6 , overlapping cooling hole geometries, a solidgeometry 78 _(solid) and a dashed geometry 78 _(dash), are illustratedfor exemplary range (α): (10°<α<30°) from row 2 of TABLE 1 withexemplary surface angles (θ_(solid)=35° and θ_(dash)=45°). It canclearly be seen that the relationship of Expressions (1) and (2)encompasses a range of distance values between a high value (d_(hi)) anda low value (d_(lo)) that are equal for the two different surface angles(θ_(solid), θ_(dash)). To achieve the same distance, in this particularcase, the dashed geometry 78 _(dash) layback angle (θ_(dash)) can have arange between 15 and 35 degrees (15°<β_(dash)<35°) while the solidgeometry 78 _(solid) layback angle (β_(solid)) can have a range between15 and 35 degrees (10°<3_(dash)<30°).

FIG. 7 , is a graph illustrating exemplary range (α): (120≤α≤16°) fromrow four of TABLE 2 for surface angle values (0°<θ<40°) representedalong the x-axis. Four lines (β_(hi), β_(lo), Δ_(hi), Δ_(lo))representing the corresponding maximum and minimum values for laybackand diffuser angles (β, Δ) are illustrated. The y-axis representscorresponding values for both the layback and diffuser angles (β, Δ) forthe respective lines (Δ_(hi), Δ_(lo), β_(hi), β_(lo)). For example, atθ=20°, Δ_(hi)=8°, Δ_(lo)=4°, β_(hi)=16°, and β_(lo)=12°, illustrated indashed line. The switch value (θ_(s)) is shown in dashed line and has avalue of (θ_(s)=28°). It should be noted that between a surface anglewith a lower value (θ_(lo)) and a surface angle with a higher value(θ_(hi)), the corresponding ranges for the layback and diffuser anglevalues (β, Δ) overlap: If θ_(lo)≤θ≤θ_(hi), then Δ_(lo)<β<β_(hi) andΔ_(lo)<Δ<β_(hi). TABLE 3 illustrates all the corresponding ranges for(α): (12≤α≤16).

TABLE 3 θ_(s) = 12° + 16° = 28° Layback angle (β) Diffuser angle (Δ) 25°≤ θ ≤ 32° 9° < β < 20° 9° < Δ < 20° θ ≤ 28° 12° ≤ β ≤ 16° Δ < 16° θ ≥28° 12° < β 12° ≤ Δ ≤ 16°

The graph illustrates how below the switch value (θ_(s)) for the surfaceangle (θ), the diffuser angle (Δ) increases in value at a first rate RIas the surface angle (θ) increases, while the layback angle (β) remainsconstant. Above the switch value (θ_(s)) of the surface angle (θ), thelayback angle (β) increases in value at the same first rate RI as thesurface angle (θ) increases, while the diffuser angle (Δ) remainsconstant.

Furthermore, a line (d_(const)) representing layback angle (β) anddiffuser angle (Δ) values corresponding with surface angle (θ) valuesfor a constant distance (d) is illustrated. Distances (d) at anglesalong line (d_(const)) have dimensions that are the same. For example, afirst cooling hole has a surface angle of θ=25°, which is less than theswitch value of θ_(s)=28°, a layback angle of β=15.3° and a diffuserangle of (25°-15.3°) or Δ=9.7°. A neighboring cooling hole has a surfaceangle of θ=32°, which is greater than the switch value of θ_(s)=28°, alayback angle of β=15.1° and a diffuser angle of (28°-15.1°) or Δ=16.9°.These two sets of values occur along the same line (d_(const)), andtherefore the first cooling hole has a distance (d) that is equal to adistance (d) of the neighboring cooling hole.

TABLE 4 generalizes all corresponding ranges for any range of anglevalues (α): (α_(low)<α<α_(hi)):

TABLE 4 α_(low) + α_(hi) = θ_(s) Layback angle (β) Diffuser angle (Δ) θ≤ θ_(s) α_(low) ≤ β ≤ α_(hi) Δ < α_(hi) θ ≥ θ_(s) α_(low) < β α_(low) ≤Δ ≤ α_(hi)

TABLE 5 gives corresponding ranges associated with a high curvatureregion of the blade 30 for 5°≤α≤40°.

TABLE 5 5° + 40° = 45° Layback angle (β) Diffuser angle (α) θ ≤ 45° 5° ≤β ≤ 40° Δ < 40° θ ≥ 45° 5° < β 5° ≤ Δ ≤ 40°

TABLE 6 gives corresponding ranges associated with a low curvatureregion of the blade 30 for 10°≤α≤20°.

TABLE 6 10° + 20° = 30° Layback angle (β) Diffuser angle (α) θ ≤ 30° 10°≤ β ≤ 20° Δ < 20° θ ≥ 30° 10° < β 10° ≤ Δ ≤ 20°

Turning to FIG. 8 , a graph illustrating the exemplary range (α):(10°≤α≤20°) from TABLE 6 for surface angle values (0°<θ<40°) representedalong the x-axis. Like FIG. 7 four lines representing the correspondingmaximum and minimum values for layback and diffuser angles (β_(hi),β_(low), Δ_(hi), Δ_(low)) are illustrated with the cross-hatch removed.Three lines (d_(const1), d_(const2), d_(const3)) representing laybackangle (β) and diffuser angle (Δ) values corresponding with surface angle(θ) values for various constant distance values (d) are illustrated.

Referring briefly back to FIG. 5 , a length (denoted “L_(β)”) betweenjunction 105 and point 107 measured along the dashed line for thediffuser angle (β) increases as the diffuser angle (β) decreases. Thelength L_(β) can be measured in terms of a hydraulic diameter (denoted“D_(h)”) of the corresponding cooling hole. Utilizing the law of sines,a relationship between the distance (d) and the angles described hereinwas found:

$\begin{matrix}{d_{const} = {\frac{D_{h}}{\sin\theta} + \frac{{L_{\beta} \cdot \sin}\beta}{\sin\Delta}}} & (3)\end{matrix}$

A first line (d_(const1)) is for when the length is twice the hydraulicdiameter (L_(β)=2D_(h)), a second line (d_(const2)) is for when thelength is equal to the hydraulic diameter (L_(β)=D_(h)), and a thirdline (d_(const3)) is for when the length is half the hydraulic diameter(L_(β)=0.5D_(h)). It can be seen that relatively higher diffuser angleswithin the range in TABLE 6 (β=19°) are associated with longer lengths(L_(β)=2D_(h)) while relatively lower diffuser angles within the samerange (β=11°) are associated with shorter lengths (L_(β)=0.5D_(h)).

Benefits associated with the distance lines within the range are a quicksolution to the problem described herein. As was previously described,to maximize cooling effectiveness, it was found to be beneficial for thefirst and second distances (d1, d2), to be consistent, that is nearlythe same or equal. Utilizing the distance lines enables more accuratecooling hole geometry and in turn higher cooling effectiveness.

Benefits associated with the ranges described herein include a quickvisualization of cooling hole geometry for different portions of theblade. Narrowing the ranges enables the manufacturing of a highperforming blade with peak performance. While narrowing the ranges toregions of possibilities saves time, money, and resources, the largestbenefit is at the system level, where higher-performing blades enableimproved system performance. Previously developed blades may peak in onearea of performance where cooling holes have the most desirable distance(d), but lose efficiency or lifetime benefits in another area ofperformance where cooling holes vary in terms of distance (d). In otherwords, the ranges considered enable the development and production ofhigher performing blades across multiple performance metrics within agiven set of constraints.

As described earlier, finding a workable solution to the nozzle-exitproblem involves finding the balance between effective cooling andaerodynamic performance by way of the cooling holes and blade geometrydescribed herein. This is a labor- and time-intensive process, becausethe process is iterative and involves the selection of various coolinghole layouts designed for (in one example) flight idle, and thenevaluating whether at other times in flight (e.g. non-flight idle) thecooling hole layout provides acceptable cooling for the blade. In someexamples, the blade may have a different pressure-side smoothnesscompared to a baseline pressure-side smoothness on which the coolinghole layout was designed. Put another way, the cooling hole layout wasoften selected accordingly for various blade configurations before acooling hole layout was found that satisfies all design requirements,e.g. cooling performance, aerodynamic performance, pressure ratio,rigidity, durability, thermal stresses, noise transmission levels, orthe like.

TABLE 7 below illustrates some cooling hole configurations that yieldedworkable solutions to the nozzle-exit wake problem.

TABLE 7 Example: 1 2 3 4 5 6 7 8 TR (in) 15.25 15.45 15.50 15.60 15.3015.65 15.70 15.75 EGT (° C.) 1090 1090 990 1020 1080 1070 1000 990 NB 6060 64 62 62 60 64 64 NN 42 42 38 40 42 40 38 38 L_(max) (in) 0.205 0.2050.253 0.219 0.224 0.245 0.235 0.253 R (in) 0.205 0.205 0.205 0.210 0.2180.217 0.220 0.205

It was discovered, unexpectedly, during the course of engine design andthe time-consuming iterative process previously described, that arelationship exists between the number of blades NB per stage, thenumber of nozzles NN per stage, the tip radius TR, the exhaust gastemperature EGT, and the blade parameter BP that yielded improvedresults. Improved results were found when a degree of flatness(represented by BP) and cooling hole distribution was tied to the numberof blades NB per stage, the number of nozzles NN per stage, the tipradius TR, and the exhaust gas temperature EGT. Whereas a cooling holepattern and degree of flatness may provide a desired result for oneengine configuration, that same combination would not necessarilyprovide the desired result for another engine configuration. Theinventors found that an improved blade performance was found not simplybased on experiments of the blade subjected to aerodynamic, thermal, anddynamic environments generally applicable to a variety of engineconfigurations. Rather, a better blade design is found when bladeproperties (flatness, e.g., FIG. 4 , and cooling hole distribution,e.g., FIGS. 5-6 ) are made dependent to the specific environment createdby the engine to which the blade is installed, which environment isrepresented by NB, NN, TR and EGT.

Such a relationship can narrow the vast range of possible blade designsdown to a range providing working solutions with a desired degree ofthermal efficiency for the specific engine configuration. Afterconducting numerous cycle tests during transient conditions (e.g.,take-off and approach), it was found that reducing a blade surfacecontour (e.g. reducing a tip shelf contour), in combination with arepeating pattern of cooling holes relative to a flat surface (where theblade parameter BP is greater than or equal to 1) at the 90-100% spanlocation on the blade, results in an highly useful and desirable bladewith respect to cooling performance, aerodynamic performance,durability, and cycle life for the blade for particular engineconfigurations.

Moreover, by utilizing this relationship, the inventors found that thenumber of suitable or feasible blades to be placed in a turbine enginethat are capable of meeting the design requirements could be greatlyreduced, thereby facilitating a more rapid down-selection of bladedesigns to consider as an engine is being developed. Such benefitprovides more insight to the requirements for a given engine, and to therequirements for particular component locations within the engine, longbefore specific technologies, integration, or system requirements aredeveloped fully. The discovered relationship also avoids or preventslate-stage redesign while also providing a blade design that integratesboth efficient performance and cooling effectiveness.

The desired relationship is represented by a blade tip durability factor(denoted “BTDF”):

$\begin{matrix}{{BTDF} = {\left( \frac{TR}{EGT} \right) \times \left( \frac{NB}{NN} \right) \times BP}} & (4)\end{matrix}$

where TR is the tip radius, EGT is the exhaust gas temperature, NB isthe number of blades per disk 32, NN is the number of nozzles 38, and BPis the blade parameter:

$\begin{matrix}{{BP} = \frac{L_{\max}}{R}} & (5)\end{matrix}$

wherein the surface length L_(max) is measured as a contour line alongthe outer wall 50 between the first and second locations L1, L2,including any local surface curvatures, and wherein the radial length Ris measured along the span-wise line between the first and secondlocations L1, L2 at the same or common chord-wise position as thesurface length L_(max). In other words, the blade parameter BP isgreater than 1 when the ratio of L_(max)/R is greater than 1 at a givenchord-wise position. As described above, the blade parameter BP isgreater than 1 when either a surface indent/recess or a surfaceprotrusion is present on the outer wall 50. Minimum and maximum valuesfor blade and engine characteristics, respectively, where expressions(4) and (5) apply and are consistent with the teachings in thedisclosure are provided below in Table 8.

TABLE 8 Parameter Minimum Value Maximum Value TR (in) 15.25 15.75 EGT (°C.) 990 1090 NB 60 64 NN 38 42 L_(max) (in) 0.205 0.253 R (in) 0.2050.224 BP 1.000 1.234 BTDF (in/° C.) 0.020 0.033

BP and BTDF values corresponding to Examples 1-8 are provided below inTable 9.

TABLE 9 Example: 1 2 3 4 5 6 7 8 BP 1.000 1.000 1.234 1.043 1.028 1.1291.068 1.234 BTDF 0.020 0.020 0.033 0.025 0.021 0.025 0.028 0.033

It was found that the range of values for BP and BTDF in TABLE 8 abovecorrelate to a generally flat blade surface without surface features 70(FIG. 3 ) while still providing desired blade cooling and performance asstated in the range for BTDF. A blade parameter BP of 1 corresponds to aperfectly flat blade outer wall, where R=L_(max) as described above.Surface protrusions or recesses, e.g. a shelf or pocket, causes L_(max)to be larger than R by more than 10% and introduces a need forredesigned cooling mechanisms for the extra surface area. The range forBP between 1-1.234 as described in TABLE 8 above allows for the bladeouter wall to have an overall smooth blade surface with minor surfaceroughness or textures present while still preserving desired cooling andperformance.

In addition, it was found that a narrowed design range for the tipradius TR being within 15.45-15.50 inches, as shown in Examples 2-3 inTABLE 7 above, provided for desirable blade cooling and performance,while the resulting narrowed minimum and maximum BTDF values did notdiffer by more than 2% from the values in TABLE 8 above.

Additional benefits associated with the BTDF described herein include aquick assessment of design parameters in terms of blade size, enginetemperature, and blade and vane numbers for engine design and particularblade design. While narrowing these multiple factors to a region ofpossibilities saves time, money, and resources, the BTDF describedherein enables the development and production of high-performanceturbine engines and blades across multiple performance metrics within agiven set of constraints.

To the extent one or more structures provided herein can be known in theart, it should be appreciated that the present disclosure can includecombinations of structures not previously known to combine, at least forreasons based in part on conflicting benefits versus losses, desiredmodes of operation, or other forms of teaching away in the art.

This written description uses examples to disclose the presentdisclosure, including the best mode, and also to enable any personskilled in the art to practice the disclosure, including making andusing any devices or systems and performing any incorporated methods.The patentable scope of the disclosure is defined by the claims, and caninclude other examples that occur to those skilled in the art. Suchother examples are intended to be within the scope of the claims if theyinclude structural elements that do not differ from the literal languageof the claims, or if they include equivalent structural elements withinsubstantial differences from the literal languages of the claims.

Further aspects of the disclosure are provided by the subject matter ofthe following clauses:

A component for a turbine engine which generates a hot gas fluid flow,and provides a cooling fluid flow, comprising a wall separating the hotgas fluid flow from the cooling fluid flow and having a heated surfacealong which the hot gas fluid flow flows and a cooled surface facing thecooling fluid flow; and at least one cooling hole comprising a passageextending between an inlet at the cooled surface and an outlet at theheated surface, the passage defining a centerline forming a first angle(θ) with the heated surface, the passage having a top wall and a bottomwall each extending from the inlet toward the outlet, and a laybacksurface defining at least a portion of the outlet, extending from thebottom wall to the heated surface, the layback surface forming a secondangle (β) with the bottom wall and a third angle (Δ) with the heatedsurface; wherein for any range of angle values (α): (αlow<α<αhi)

If αhi+αlow<θ, then αlow<Δ<αhi; and

If αhi+αlow>θ, then αlow<β<αhi.

The component of any preceding clause wherein the range of angle valuesis 12°<α<16°.

The component of any preceding clause wherein the range of angle valuesis 10°<α<20°.

The component of any preceding clause wherein the range of angle valuesis 5°<α<40°.

The component of any preceding clause wherein the layback surfaceintersects the heated surface at a downstream end of the outlet, the topwall intersects the heated surface at an upstream end of the outlet anda straight-line distance measured from the downstream end to theupstream end defines a first dimension of the outlet.

The component of any preceding clause wherein the at least one coolinghole is multiple cooling holes with each having first dimensions within5% of each other.

The component of any preceding clause wherein the second angle (β) andthe third angle (Δ) have an interdependent relationship.

The component of any preceding clause wherein as the first angle (θ)increases to a switch value (θ_(s)), one of the second angle (β) or thethird angle (Δ) increases at a first rate while the other of the secondangle (β) or the third angle (Δ) remains constant.

The component of any preceding clause wherein as the first angle (θ)increases above the switch value (θs), the other of the second angle (β)and the third angle (Δ) increases at the first rate while the other ofthe second angle (β) and the third angle (Δ) remains constant.

The component of any preceding clause located within a turbine engine,comprising an engine core extending along an engine centerline andincluding a compressor section, a combustor, and a turbine section inaxial flow arrangement and defining a flow path; a temperature sensorwithin the engine and configured to detect an exhaust gas temperature(EGT) within the engine core; a set of nozzles circumferentiallyarranged in the turbine section and defining a number of nozzles (NN);and a set of blades circumferentially arranged in the turbine sectionadjacent to, and downstream of, the set of nozzles, the set of bladesdefining a number of blades (NB); wherein a blade in the set of bladescomprises an outer wall bounding an interior and having an exteriorsurface, with the outer wall defining a pressure side and a suction sideand extending between a leading edge and a trailing edge to define achord-wise direction, and also extending between a tip and a root todefine a span-wise direction; a cooling conduit within the interior; atip radius (TR) defined between the engine centerline and the tip understandard day conditions of 15° C. at mean sea level altitude and 101.3kPa atmospheric pressure; a radial length (R) defined by a span-wiseline extending between a first location on the outer wall and a secondlocation on the outer wall, with the first location and the secondlocation having a common chord-wise position; a surface length (L_(max))defined by a contour line along the outer wall between the firstlocation and the second location at the common chord-wise position; anda blade parameter (BP) defined as a ratio of the surface length to theradial length (BP=L_(max)/R); wherein the exhaust gas temperature EGT,the number of blades NB, the number of nozzles NN, the tip radius TR,and the blade parameter BP define a blade tip durability factor (BTDF)by the following expression BTDF=(TR/EGT)×(NB/NN)×BP; wherein the bladetip durability factor BTDF is between 0.020 and 0.033 in/° C., and theblade parameter BP is between 1-1.234.

A blade for a turbine engine which generates a hot gas fluid flow, andprovides a cooling fluid flow, comprising a wall separating the hot gasfluid flow from the cooling fluid flow and having a heated surface alongwhich the hot gas fluid flow flows and a cooled surface facing thecooling fluid flow; and a plurality of cooling holes each comprising apassage extending between an inlet at the cooled surface and an outletat the heated surface, the outlet extending between an upstream end anda downstream end with respect to the hot gas fluid flow to define astraight-line distance, the passage defining a centerline forming afirst angle (θ) with the heated surface; wherein the distances for eachof the plurality of cooling holes is maintained within 5% of each otheras the first angle (θ) increases regardless of the location of thecooling hole on the blade.

The blade of any preceding clause wherein the passage further comprisesa top wall and a bottom wall each extending from the inlet toward theoutlet, and a layback surface defining at least a portion of the outlet,extending from the bottom wall to the heated surface, the laybacksurface forming a second angle (θ) with the bottom wall and a thirdangle (Δ) with the heated surface, wherein for any range of angle values(α): (αlow<α<αhi)

If αhi+αlow<θ, then αlow<Δ<αhi; and

If αhi+αlow>θ, then αlow<β<αhi

The blade of any preceding clause wherein the range of angle values is12°<α<16°.

The blade of any preceding clause wherein the range of angle values is10°<α<20°.

The blade of any preceding clause wherein the range of angle values is5°<α<40°.

The blade of any preceding clause wherein as the first angle (θ)increases to a switch value (θs) one of the second angle (β) and thethird angle (Δ) increases at a first rate while the other of the secondangle (β) and the third angle (Δ) remains constant.

The blade of any preceding clause wherein as the first angle (θ)increases above the switch value (θs) the other of the second angle (β)and the third angle (Δ) increases at the first rate while the other ofthe second angle (β) and the third angle (Δ) remains constant.

The blade of any preceding clause wherein the layback surface intersectsthe bottom wall at a junction and a length (Lβ) measured along the firstangle (θ) from the junction to the straight-line distance increases whenthe second angle (β) increases.

The blade of any preceding clause wherein the passage further defines ahydraulic diameter (Dh) and for any constant distance (dconst), first,second, and third angles satisfy the following expression:d_(const)=(D_(h)/sin θ)+((L_(β)·sin β)/sin Δ)

The blade of any preceding clause wherein the plurality of cooling holesis three or more cooling holes.

1. A component for a turbine engine which generates a hot gas fluidflow, and provides a cooling fluid flow, comprising: a wall separatingthe hot gas fluid flow from the cooling fluid flow and having a heatedsurface along which the hot gas fluid flow flows and a cooled surfacefacing the cooling fluid flow; and a set of cooling holes, each coolinghole of the set of cooling holes comprising a passage extending betweenan inlet at the cooled surface and an outlet at the heated surface, thepassage defining a centerline forming a first angle (θ) with the heatedsurface, the passage having a top wall and a bottom wall each extendingfrom the inlet toward the outlet, and a layback surface defining atleast a portion of the outlet, extending from the bottom wall to theheated surface, the layback surface forming a second angle (β) with thebottom wall and a third angle (Δ) with the heated surface; wherein forany range of angle values (α): (α_(low)<α<α_(hi)); for at least a firstcooling hole of the set of cooling holes α_(hi)+α_(low)≤θ, andα_(low)<Δ<α_(hi); and for at least a second cooling hole of the set ofcooling holes α_(hi)+α_(low)≥θ, and α_(low)<β<α_(hi).
 2. The componentof claim 1 wherein the range of angle values is 12°<α<16°.
 3. Thecomponent of claim 1 wherein the range of angle values is 100<α<20°. 4.The component of claim 1 wherein the range of angle values is 5°<α<40°.5. The component of claim 1 wherein the layback surface intersects theheated surface at a downstream end of the outlet, the top wallintersects the heated surface at an upstream end of the outlet and astraight-line distance measured from the downstream end to the upstreamend defines a first dimension of the outlet.
 6. The component of claim 5wherein the set of cooling holes includes multiple cooling holes witheach cooling hole having first dimensions within 5% of each othercooling hole.
 7. The component of claim 1 wherein the second angle (β)and the third angle (Δ) have an interdependent relationship.
 8. Thecomponent of claim 7 wherein as the first angle (θ) increases to aswitch value (θ_(s)), one of the second angle (β) or the third angle (Δ)increases at a first rate while the other of the second angle (β) or thethird angle (Δ) remains constant.
 9. The component of claim 8 wherein asthe first angle (θ) increases above the switch value (θ_(s)), the otherof the second angle (β) and the third angle (Δ) increases at the firstrate while the other of the second angle (β) and the third angle (Δ)remains constant.
 10. The component of claim 1 located within a turbineengine, comprising: an engine core extending along an engine centerlineand including a compressor section, a combustor, and a turbine sectionin axial flow arrangement and defining a flow path; a temperature sensorwithin the engine and configured to detect an exhaust gas temperature(EGT) within the engine core; a set of nozzles circumferentiallyarranged in the turbine section and defining a number of nozzles (NN);and a set of blades circumferentially arranged in the turbine sectionadjacent to, and downstream of, the set of nozzles, the set of bladesdefining a number of blades (NB); wherein a blade in the set of bladescomprises: an outer wall bounding an interior and having an exteriorsurface, with the outer wall defining a pressure side and a suction sideand extending between a leading edge and a trailing edge to define achord-wise direction, and also extending between a tip and a root todefine a span-wise direction; a cooling conduit within the interior; atip radius (TR) defined between the engine centerline and the tip understandard day conditions of 15° C. at mean sea level altitude and 101.3kPa atmospheric pressure; a radial length (R) defined by a span-wiseline extending between a first location on the outer wall and a secondlocation on the outer wall, with the first location and the secondlocation having a common chord-wise position; a surface length (L_(max))defined by a contour line along the outer wall between the firstlocation and the second location at the common chord-wise position; anda blade parameter (BP) defined as a ratio of the surface length to theradial length (BP=L_(max)/R); wherein the exhaust gas temperature EGT,the number of blades NB, the number of nozzles NN, the tip radius TR,and the blade parameter BP define a blade tip durability factor (BTDF)by the following expression:${{BTDF} = {\left( \frac{TR}{EGT} \right) \times \left( \frac{NB}{NN} \right) \times {BP}}};$wherein the blade tip durability factor BTDF is between 0.020 and 0.033in/° C., and the blade parameter BP is between 1-1.234.
 11. A blade fora turbine engine which generates a hot gas fluid flow, and provides acooling fluid flow, comprising: a wall separating the hot gas fluid flowfrom the cooling fluid flow and having a heated surface along which thehot gas fluid flow flows and a cooled surface facing the cooling fluidflow; and a plurality of cooling holes each comprising a passageextending between an inlet at the cooled surface and an outlet at theheated surface, the outlet extending between an upstream end and adownstream end with respect to the hot gas fluid flow to define astraight-line distance, the passage defining a centerline forming afirst angle (θ) with the heated surface, a top wall, and a bottom walleach extending from the inlet toward the outlet, and a layback surfacedefining at least a portion of the outlet, extending from the bottomwall to the heated surface, the layback surface forming a second angle(β) with the bottom wall and a third angle (Δ) with the heated surface,wherein for any range of angle values (α): (α_(low)<α<α): for at least afirst cooling hole of the plurality of cooling holes α_(hi)+α_(low)<θ,and α_(low)<Δ<α_(hi), and for at least a second cooling hole of theplurality of cooling holes α_(hi)+α_(low)>θ, and α_(low)<β<α_(hi);wherein the distances for each of the plurality of cooling holes ismaintained within 5% of each other as the first angle (θ) increasesregardless of the location of the cooling hole on the blade. 12.(canceled)
 13. The blade of claim 11 wherein the range of angle valuesis 12°<α<16°.
 14. The blade of claim 11 wherein the range of anglevalues is 10°<α<20°.
 15. The blade of claim 11 wherein the range ofangle values is 5°<α<40°.
 16. The blade of claim 11 wherein as the firstangle (θ) increases to a switch value (θ_(s)) one of the second angle(β) and the third angle (Δ) increases at a first rate while the other ofthe second angle (β) and the third angle (Δ) remains constant.
 17. Theblade of claim 16 wherein as the first angle (θ) increases above theswitch value (θ_(s)) the other of the second angle (β) and the thirdangle (Δ) increases at the first rate while the other of the secondangle (β) and the third angle (Δ) remains constant.
 18. The blade ofclaim 11 wherein the layback surface intersects the bottom wall at ajunction and a length (L_(β)) measured along the first angle (θ) fromthe junction to the straight-line distance increases when the secondangle (β) increases.
 19. The blade of claim 18 wherein the passagefurther defines a hydraulic diameter (D_(h)) and for any constantdistance (d_(const)), first, second, and third angles satisfy thefollowing expression:$d_{const} = {\frac{D_{h}}{\sin\theta} + \frac{{L_{\beta} \cdot \sin}\beta}{\sin\Delta}}$20. (canceled)
 21. The component of claim 1, wherein each cooling holeof the set of cooling holes for any range of angle values (α):(α_(low)<α<α_(hi)), satisfies at least one of the following:if α_(hi)+α_(low)≤0, and α_(low)<Δ<α_(hi); andif α_(hi)+α_(low)≥0, and α_(low)<β<α_(hi).